Faraday's law of induction and Related Topics

Alternating electric current flows through the solenoid on the left, producing a changing magnetic field. This field causes, by electromagnetic induction, an electric current to flow in the wire loop on the right.

Electromagnetic induction

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Production of an electromotive force across an electrical conductor in a changing magnetic field.

Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current that flows through the small coil (A), creating a magnetic field. When the coils are stationary, no current is induced. But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G).

A diagram of Faraday's iron ring apparatus. Change in the magnetic flux of the left coil induces a current in the right coil.

The longitudinal cross section of a solenoid with a constant electrical current running through it. The magnetic field lines are indicated, with their direction shown by arrows. The magnetic flux corresponds to the 'density of field lines'. The magnetic flux is thus densest in the middle of the solenoid, and weakest outside of it.

Rectangular wire loop rotating at angular velocity ω in radially outward pointing magnetic field B of fixed magnitude. The circuit is completed by brushes making sliding contact with top and bottom discs, which have conducting rims. This is a simplified version of the drum generator.

Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction.

U.S. NRC image of a modern steam turbine generator (STG).

Electric generator

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Device that converts motive power into electric power for use in an external circuit.

Early Ganz Generator in Zwevegem, West Flanders, Belgium

The Faraday disk was the first electric generator. The horseshoe-shaped magnet (A) created a magnetic field through the disk (D). When the disk was turned, this induced an electric current radially outward from the center toward the rim. The current flowed out through the sliding spring contact m, through the external circuit, and back into the center of the disk through the axle.

Hippolyte Pixii's dynamo. The commutator is located on the shaft below the spinning magnet.

This large belt-driven high-current dynamo produced 310 amperes at 7 volts. Dynamos are no longer used due to the size and complexity of the commutator needed for high power applications.

Ferranti alternating current generator, c. 1900.

A small early 1900s 75 kVA direct-driven power station AC alternator, with a separate belt-driven exciter generator.

The Athlone Power Station in Cape Town, South Africa

Hydroelectric power station at Gabčíkovo Dam, Slovakia

Hydroelectric power station at Glen Canyon Dam, Page, Arizona

Protesters at Occupy Wall Street using bicycles connected to a motor and one-way diode to charge batteries for their electronics

The principle, later called Faraday's law, is that an electromotive force is generated in an electrical conductor which encircles a varying magnetic flux.

Transformer

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Passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits.

Ideal transformer connected with source VP on primary and load impedance ZL on secondary, where 0 < ZL < ∞.

Instrument transformer, with polarity dot and X1 markings on low-voltage ("LV") side terminal

Power transformer overexcitation condition caused by decreased frequency; flux (green), iron core's magnetic characteristics (red) and magnetizing current (blue).

Laminated core transformer showing edge of laminations at top of photo

Interleaved E-I transformer laminations showing air gap and flux paths

Laminating the core greatly reduces eddy-current losses

Windings are usually arranged concentrically to minimize flux leakage.

Cut view through transformer windings.
Legend:
White: Air, liquid or other insulating medium
Green spiral: Grain oriented silicon steel
Black: Primary winding
Red: Secondary winding

Cutaway view of liquid-immersed transformer. The conservator (reservoir) at top provides liquid-to-atmosphere isolation as coolant level and temperature changes. The walls and fins provide required heat dissipation.

Substation transformer undergoing testing.

An electrical substation in Melbourne, Australia
showing three of five 220 kV – 66 kV transformers, each with a capacity of 150 MVA

Transformer at the Limestone Generating Station in Manitoba, Canada

Schematic of a large oil-filled power transformer 1. Tank 2. Lid
3. Conservator tank 4. Oil level indicator 5. Buchholz relay for detecting gas bubbles after an internal fault 6. Piping
7. Tap changer 8. Drive motor for tap changer 9. Drive shaft for tap changer
10. High voltage (HV) bushing
11. High voltage bushing current transformers
12. Low voltage (LV) bushing
13. Low voltage current transformers
14. Bushing voltage-transformer for metering
15. Core 16. Yoke of the core
17. Limbs connect the yokes and hold them up 18. Coils
19. Internal wiring between coils and tapchanger
20. Oil release valve
21. Vacuum valve

Faraday's experiment with induction between coils of wire

Induction coil, 1900, Bremerhaven, Germany

Shell form transformer. Sketch used by Uppenborn to describe ZBD engineers' 1885 patents and earliest articles.

Core form, front; shell form, back. Earliest specimens of ZBD-designed high-efficiency constant-potential transformers manufactured at the Ganz factory in 1885.

The ZBD team consisted of Károly Zipernowsky, Ottó Bláthy and Miksa Déri

Stanley's 1886 design for adjustable gap open-core induction coils

"E" shaped plates for transformer cores developed by Westinghouse

Faraday's law of induction, discovered in 1831, describes the induced voltage effect in any coil due to a changing magnetic flux encircled by the coil.

Magnetic field

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Vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

Right hand grip rule: a current flowing in the direction of the white arrow produces a magnetic field shown by the red arrows.

A Solenoid with electric current running through it behaves like a magnet.

A sketch of Earth's magnetic field representing the source of the field as a magnet. The south pole of the magnetic field is near the geographic north pole of the Earth.

One of the first drawings of a magnetic field, by René Descartes, 1644, showing the Earth attracting lodestones. It illustrated his theory that magnetism was caused by the circulation of tiny helical particles, "threaded parts", through threaded pores in magnets.

Hans Christian Ørsted, Der Geist in der Natur, 1854

are called the Ampère–Maxwell equation and Faraday's law respectively.

Gauss's law for magnetism: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current.

Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.

In a geomagnetic storm, a surge in the flux of charged particles temporarily alters Earth's magnetic field, which induces electric fields in Earth's atmosphere, thus causing surges in electrical power grids. (Not to scale.)

Magnetic-core memory (1954) is an application of Ampère's law. Each core stores one bit of data.

Left: A schematic view of how an assembly of microscopic dipoles produces opposite surface charges as shown at top and bottom. Right: How an assembly of microscopic current loops add together to produce a macroscopically circulating current loop. Inside the boundaries, the individual contributions tend to cancel, but at the boundaries no cancelation occurs.

The Maxwell–Faraday version of Faraday's law of induction describes how a time-varying magnetic field corresponds to curl of an electric field.

A typical reaction path requires the initial reactants to cross an energy barrier, enter an intermediate state and finally emerge in a lower energy configuration. If charge separation is involved, this energy difference can result in an emf. See Bergmann et al. and Transition state.

Electromotive force

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Electrical action produced by a non-electrical source, measured in volts.

The equivalent circuit of a solar cell; parasitic resistances are ignored in the discussion of the text.

Solar cell voltage as a function of solar cell current delivered to a load for two light-induced currents IL; currents as a ratio with reverse saturation current I0. Compare with Fig. 1.4 in Nelson.

The general principle governing the emf in such electrical machines is Faraday's law of induction.

Lorentz force

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Combination of electric and magnetic force on a point charge due to electromagnetic fields.

Lorentz' theory of electrons. Formulas for the Lorentz force (I, ponderomotive force) and the Maxwell equations for the divergence of the electrical field E (II) and the magnetic field B (III), La théorie electromagnétique de Maxwell et son application aux corps mouvants, 1892, p. 451. V is the velocity of light.

Charged particle drifts in a homogeneous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (e.g. gravity) (D) In an inhomogeneous magnetic field, grad H

Right-hand rule for a current-carrying wire in a magnetic field B

Lorentz force -image on a wall in Leiden

Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a moving charged particle.

Michael Faraday

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English scientist who contributed to the study of electromagnetism and electrochemistry.

Portrait of Faraday in his late thirties, ca. 1826

Three Fellows of the Royal Society offering the presidency to Faraday, 1857

Michael Faraday's grave at Highgate Cemetery, London

Equipment used by Faraday to make glass on display at the Royal Institution in London

Electromagnetic rotation experiment of Faraday, ca. 1821

One of Faraday's 1831 experiments demonstrating induction. The liquid battery (right) sends an electric current through the small coil (A). When it is moved in or out of the large coil (B), its magnetic field induces a momentary voltage in the coil, which is detected by the galvanometer (G).

A diagram of Faraday's iron ring-coil apparatus

Built in 1831, the Faraday disk was the first electric generator. The horseshoe-shaped magnet (A) created a magnetic field through the disk (D). When the disk was turned, this induced an electric current radially outward from the center toward the rim. The current flowed out through the sliding spring contact m, through the external circuit, and back into the center of the disk through the axle.

Faraday (right) and John Daniell (left), founders of electrochemistry.

Faraday holding a type of glass bar he used in 1845 to show magnetism affects light in dielectric material.

Michael Faraday meets Father Thames, from Punch (21 July 1855)

Faraday's apparatus for experimental demonstration of ideomotor effect on table-turning

Faraday delivering a Christmas Lecture at the Royal Institution in 1856.

Statue of Faraday in Savoy Place, London. Sculptor John Henry Foley RA.

Plaque erected in 1876 by the Royal Society of Arts at 48 Blandford Street, Marylebone, London

Michael Faraday in his laboratory, c. 1850s.

Michael Faraday's study at the Royal Institution.

Michael Faraday's flat at the Royal Institution.

Artist Harriet Jane Moore who documented Faraday's life in watercolours.

Portrait of Faraday in 1842 by Thomas Phillips

His demonstrations established that a changing magnetic field produces an electric field; this relation was modelled mathematically by James Clerk Maxwell as Faraday's law, which subsequently became one of the four Maxwell equations, and which have in turn evolved into the generalization known today as field theory.

Inductor

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Passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it.

Example of signal filtering. In this configuration, the inductor blocks AC current, while allowing DC current to pass.

Example of signal filtering. In this configuration, the inductor decouples DC current, while allowing AC current to pass.

Collection of RF inductors, showing techniques to reduce losses. The three top left and the ferrite loopstick or rod antenna, bottom, have basket windings.

A variety of types of ferrite core inductors and transformers

Laminated iron core ballast inductor for a metal halide lamp

Toroidal inductor in the power supply of a wireless router

A "roller coil", an adjustable air-core RF inductor used in the tuned circuits of radio transmitters. One of the contacts to the coil is made by the small grooved wheel, which rides on the wire. Turning the shaft rotates the coil, moving the contact wheel up or down the coil, allowing more or fewer turns of the coil into the circuit, to change the inductance.

An MF or HF radio choke for tenths of an ampere, and a ferrite bead VHF choke for several amperes.

When the current flowing through the coil changes, the time-varying magnetic field induces an electromotive force (e.m.f.) (voltage) in the conductor, described by Faraday's law of induction.